Resistivity



1957 A A. STRIPLING R 24,280

ACOUSTIG VELOCITY-ELECTRICAL RESISTANCE CORRELATION WELL LOGGING Original Filed June 29, 1953 2 Sheets-Sheet l ALLEN AD 5' THIPL ING' 1N VEN TOR.

' BY xQ/um ATTUHNEY Feb. 19, 1957 A. A. STRIPLING 24,280

ACOUSTIC VELOCITY-ELECTRICAL RESISTANCE CORRELATION WELL LOGGING Origmal Filed June 29, 1953 2 Sheets-Sheet 2 PEPQODUCEI? //4\ 0 coMpz/rsR RECORDER v I /05 //5 0 I 1 15a m2 //3 J YNTA/ET/C RR/MARY /04 L06 ALLEN A n STHIPLINB IN VEN TOR.

BY 0. ,6, W

ATTUHNEY United States Patent 24,280 ACOUSTIC VELOCITY-ELECTRICAL RESISTANCE CORRELATION WELL LOGGING Allen A. Stripling, Dallas, Tex., assignor, by mesne assignments, to Socony Mobil Oil Company, Inc., New York, N. Y., a corporation of New York Original No. 2,713,147, dated July 12, 1955, Serial No. 364,717, June 29, 1953. Application for reissue December 3, 1956, Serial No. 626,571

14 Claims. (Cl. 324-1) Matter enclosed in heavy brackets appears in the original patent but forms no part of this reissue specification; matter printed in italics indicates the additions made by reissue.

This invention relates to well logging and more particularly to a correlation between acoustic and electrical well data.

Acoustic and electrical properties of earth formations have been measured and found to vary in a manner controlled by structural features and fluid content. In connection with the location of petroleum deposits in subsurface formations, it is important to delineate formations saturated with petroliferous liquids containing petroleum from formations containing nonpetroliferous liquids. Early efiorts produced useful logs of electrical resistance and the spontaneous potentials encountered in a well bore both now widely used. Following more recent developments a method of accurately measuring the acoustic velocity of such formations has been perfected.

In accordance with the present invention, it has been discovered that correlation between an electrical log and an acoustic log, or the lack of correlation therebetween, provides an indication as to the nature of liquids in formations in a given location or earth section penetrated by a bore hole.

In accordance with the present invention, earth formations, particularly those formations having abnormal fluid content, are delineated by generating two signals which vary as a function of depth in accordance with two earth controlled parameters, one of which is an electrical resistivity function and the other, an acoustic velocity function of the formations. A synthetic signal is generated which varies in dependence upon a power function, an assumed normal saturation of the formations, and one of the generated signals. The synthetic signal and the second of the two signals are recorded as functions of depth to indicate by departures therebetween earth sec tions having abnormal fluid content.

In a more specific aspect of the invention a resistivity function and a velocity function, both of which vary with depth, are correlated by producing from one of them a synthetic function derived either from the resistivity or the velocity function wherein the relationship between resistivity and velocity may be shown to be of the form V=K(RZ) where V is acoustic velocity;

K is a constant depending upon an assumed character of fluids in the formations;

R is the measured resistivity of the formations;

Z is the depth; and

a is a constant.

In accordance with a further aspect of the invention, a system is provided for translating a resistivity function to an equivalent acoustic velocity function, or vice versa, in order to produce a synthetic function on a basis immediately comparable to a measured function. Further,

means are provided for producing a log of the difference between a measured and a synthetic function.

For a further understanding of the present invention ICC and for further objects and advantages thereof, reference may now be had to the following description taken in conjunction with the accompanying drawings in which:

Fig. 1 diagrammatically illustrates a system for derivation of a synthetic log;

Fig. 2 illustrates in greater detail operation of a portion of the system of Fig. l; v

Fig. 3 illustrates a mechanical system for raising a function to a power;

Fig. 4 illustrates use of reproducible logs in accordance with the present invention; and

Fig. 5 illustrates an alternative form of system for obtaining a resistivity function.

The present invention may best be appreciated if it is understood that it relates to the production of a synthetic function based upon primary data obtained by one of the two methods outlined below:

1.--VELOCITY FUNCTION In accordance with a first method, and as described in detail in co-pending application Serial No. 192,750, now Patent No. 2,704,364, of Gerald C. Summers, a coworker of applicants, primary data such as the time At required for an acoustic pulse to travel from a pulse source it) positioned in a bore [holl] hole 11 through adjacent formations to a pulse receiver 12 spaced a fixed distance from source 10 is measured and plotted as a function of depth on a chart 13 by means of a suitable recording device 14. More particularly, electrical pulses from source 10 are transmitted to a translating circuit 15 upon production of each of a series of acoustic pulses from the source 10. Upon receipt of each of the acoustic pulses by receiver 12 an electrical pulse is transmitted to circuit 15. A voltage is developed at the output terminals of circuit 15 and applied to a recording drive mechanism such as a motor 16. This output voltage is maintained at all times proportional to the time interval between each pair of electrical pulses applied to circuit 15. A measuring pulley 17 actuated by cable 18, which supports pulser 10 and receiver 12, is coupled as generically illustrated by the dotted line 19 to the chart drive shaft 20 to move chart 13 past a recording pen 14a in dependence upon movement of the pulser 10 and receiver 12 along the length of the bore hole. Thus, there is produced a line graph 21 which shows variations in incremental acoustic travel time (At) as a function of bore hole depth.

2, RESISTIVITY FUNCTION The second method of logging to obtain primary data involves measurement of the electrical resistivity of the adjacent formations. Of the several different specific procedures for making such measurements, the system shown in Fig. 1 is suitable and involves passing current from a generator 25 through the earth between a surface electrode 26 positioned near the mouth of the bore hole 11 and a second electrode 27 movably supported in the bore hole. The current between electrodes 26 and 27 is maintained constant by control of generator 25. The voltage appearing between detecting electrode 29 and the surface electrode 26 due to such current flow is applied to a metering circuit 30. The foregoing is known as a long normal electrode configuration in which variations in the resistance of formations penetrated by bore hole 11 then appear as variations in the voltage applied to produce an indication on meter 30a. A voltage suitable for driving a chart recording mechanism 31 is thus developed and applied by way of channel 30b to the drive motor 32 of a chart recorder 33. There is thus produced on chart 34 a line graph 35 of electrical earth resistance which shows resistivity variations as a function of depth. The drive shaft 36 for chart 34 is coupled to measuring pulley 17 so that the depth scalecorrespondswith the depth scale on chart 34.

The foregoingbriefly describesrepresentative--methodsof measuring the acoustic velocity function (incremental travel time) of earth formations penetrated by a bore hole and for measuring an electrical resistivity function. The foregoing is to be taken as-suggestive of suitable systems and not by way of limitation. The present invention contemplates utilization of data such as appears on the At log chart 13 and the resistivity'log chart 34' so long as they are compatible under the conditions hereinafter set forth.

It has'been foundthat for'normal conditions as to fluid content of formations penetrated by the bore hole there is an empirical relationship between the line graphs 21 and 35 that may be derived from the Equation 1, namely or K A from which it. will be. seen that 1 K'K & r-(22 or KII a R- [rm-gut 2 where At is a velocity function, specifically the incremental travel time: function corresponding with line graph 21; R is electrical resistivity, specifically line graph 35; Z is the depth function, specifically the length of charts 13 and [35134;

[K]K" is a constant depending upon as assumed fluid condition in the formations; and

[a]a' is a mathematical power function.

It has been found that if the fluid conditions in the bore hole conform precisely to the assumed normal conditions, then the data plotted on log 13 may be translated to reproduce substantially the resitivity log plotted on chart 34. It is also apparent that the resistivity log may be. translated into avelocity log. That is, for normal conditions one log may be predicted from the. other prov ducing a synthetic log. However where the fluid content of the earth formations differs from the assumed normal conditions, there will be substantial divergence as illustrated by the differences between the resistivity, log on chart 34vanda synthetic resistivity log, for example as shown on chart 71 predicted. from the, At log.

. If formation fluids of normal salinity are assumed and a synthetic. resistivity log predicted from a At log, the synthetic log. will diverge. in a first sense. from measured values of resistivity where the measurements are made, adjacent: a formation saturated with a com centrated. salt solution. Similarly, there. will be divergence in a second and opposite sense. from measurements-made adjacent formations saturated with highly resistive liquids such. as hydrocarbons or fresh water.

Synthetic resistivity log There will' now be described the method and a system for producing a synthetic resistivity log which is dependent upon a velocity function, the At log 21, on chart 13; A value. of. one-sixth A.) will be assumed for the exponent ['a..] a" of Equation 2.

The At function appearing as avoltage at the output terminals of .circuit 15? is applied to, terminals, 40 of a differential servo-amplifier 41' aswell' as to the chart recording motor 116. The outputvoltage from servo-amplh is connected to ground.

fier 41 appearing in channel 42 is applied to a motor 43 Which-is mechanically coupled, as indicated by the dotted line 44, to the variable taps on each of six potentiometers 45, 46, 47, 48, 49 and 50. Each of the otentiometers 45-50 has its left hand terminal connected to ground. The right hand terminal of potentiometer 45 is can nected by way'ofa voltage source 51 to'ground so that a fi xed current flows through the potentiometer 45'. The variable tap-45a" i's-connected by way ofan isolating network or stage 45b, for example a cathode follower, to the right hand terminal' of" the: next succeeding potentiometer 46. The tap4'6a similarly is, connected: to potentiometer 47 which inturn is, connectedto potentiometer 48 and thence to otentiometers 49"and 50. The tap 50s on potentiometer-fil is-connected by wayof conductor 52 to one of the-second pair of; inputtenninals 53 on servo-amplifier 41'; The second of input terminals 53 It can be shown that the voltage appearing. between; tap 5.0; and. ground may be expressed: by the: following equation:

0 6 esp-F01 T where When the latter voltage. isv applied to the second input terminalof thevdiiferential servo-amplifier 41, it canv then be shown that the ratio incur a 6 61 In other words, the rotation of motor 43 is proportional to the sixth root of eAt. Thus there is computed one of the variables of Equation 2 from the velocity function At shown as line graph 21.

The voltage driving. motor 43 also is proportional to the sixth root of eAt. Thus there is computed one of the variables of Equation 2. from the velocity function At shown as line graph-21.

The voltage drivingmotor 43 also is proportional to the sixth root of eAt. The latter'voltage is connected by way of channel 55 and isolating stage or network 56 to a recording. drive motor 57. A voltage is added to they output of network 56'. from a second source 60.- Source 60: is connected. in series with a potentiometer 61. One output conductor from network SG is'cQnnected to the variable tap62, onv potentiometer 61. The fixed tap on potentiometer 61 is connected by way of conductor 63 to; one terminal ofmotor 5.7. The second output conductor 64-fr.om,network. 56 is connected directly to the second terminal of; motor 57.

Thevariabletap 62. on potentiometer 61' is driven in direct proportion to the depth of the associated exploring instruments iii-bore hole 11 as indicated by the mechanical coupling, the dotted line 65. Thus there is added to the output of network 56 a voltage which de creases linearly as the depth of the exploring instrument in bore hole 11 increases. two variables of Equation 2 is provided for actuating motor 57 so that the line graph 70 on chart 71 is a synthetic resistivity log: based upon (1) the velocity function, At, (2) a power function, (3) a depth function and (4) an assumed normal saturation of the formations, the factor K of Equation (2). For those portions of the synthetic restivity log related to formations having normal saturation, the synthetic resistivity log conforms to Within a first degree. with the measured resistivity log shown on chartl34. However where there are abnormal or anomalous fluid, conditions in the bore hole, there will be divergencev between, the, two logs. While. as H- lustrated. there. are. points of noticeable divergence, a

By this means the second of differential resistivity log, a log of the differences between a measured and a synthetic resistivity 10g, more clearly emphasizes those differences.

Differential resisitivity log Having obtained a synthetic resistivity function and a measured resistivity function, a differential resistivity function may then be obtained by combining the voltages in opposite senses and applying the algebraic sum to a fourth recorder drive motor 75. More particularly, the voltage applied to motor 57, the synthetic resistivity function, is connected to an isolating stage or network 76. Similarly, the measured resistivity function applied to motor 32 is also applied to an isolating stage or network 77. Conductor 78 directly interconnects one output terminal of each of networks 76 and 77. Conductor 79 is connected between the second output terminal of network 76 and one terminal of motor 75. Conductor 80 is connected to the second output terminal of network 77 and to the second terminal of motor 75. The voltages at the outputs of networks 76 and 77 are thus phased and sensed as to be in opposition so that the differences between the voltages are effective in driving motor 75 thereby to produce a line graph 81 truly representative of the differences between line graphs 70 and 35. It will thus be seen that the divergences from a central zero line are readily related to the apparent differences in the line graphs 70 and 35.

In Fig. 2 the potentiometer system used for extracting the sixth root of the At function has been illustrated in greater detail. A shaft 43a, for example the shaft of motor 43, is directly connected to each of the taps 45a- 50a of the potentiometers 45-50. Each of the potentiometers is connected at one extremity to ground. Each variable tap is connected through an isolating network, such as network 45b, to the extremity of the next succeeding potentiometer. The related angles and 0m determine the nature of the output. If an input voltage e1 is applied to potentiometer 45, then the voltage era is proportional to the sixth power of the ratio of This basic system may be used either to raise one of the desired functions to a power or to extract a root of one of the desired functions and is essentially an electromechanical computing network that is used as an element of the system of Fig. 1 to extract the sixth root of the At function. If desired, the same system may be utilized to raise a resistivity function to the sixth power in the production of a synthetic At log, a process exactly the reverse of that above described in the production of a synthetic resistivity log. Using the system of Fig. 2 as an element in producing a synthetic At log, the angle 0 must be varied in proportion to the product of the resistivity function and a linearly increasing depth function in a manner well understood by those skilled in the art.

Fig. 3 illustrates a mechanical system for obtaining a power or a root from a given function and comprises a pair of rollers 85 and 86 rotatably mounted in a housing 87. The first roller 85 is simply a cylinder of a selected diameter. The roller 86 is a cone shaped member having a spiral groove 88 cut in the surface thereof. A pair of cords or cables 89 and 90 of equal length are wound on the two rollers 85 and 86. Cord 89 is fastened at one extremity at point 85a on roller 85 and at its other extremity'at point 86a on roller 86. Cord 90 is fastened at one extremity at point 85b on roller 85 and at the other extremity at point 86b on roller 86. By properly selecting the slope or the change in radius per unit length of the roller 86, the output from the shaft of roller 85 may be a selected power function of the input description of the operation of the mechanical system for obtaining a power or a root of a function, reference may be had to Computing Mechanisms and Linkages by Svoboda, volume 27, M. I. T. Radiation Series, Mc- GraW-Hill, 1948, page 21 et seq.

Referring now to Fig. 4, a system is illustrated which utilizes a phonographically reproducible primary log, either a resistivity log or a At log, for the production of a synthetic log. The primary log is passed through a reproducer 101, and an output signal proportional to the function recorded on the primary log is applied to a computer 102 Whose output in turn is applied to a recorder 103 to produce the synthetic log 104. The re producer 101 and recorder 103 may be of any type well known in the art. The computer may be of the type above described in connection with Fig. l or any equivalent device for carrying out the computations indicated by Equations 1 or 2 for predicting a resistivity function from a velocity function or a velocity function from the resistivity function.

It will thus be seen that there may be produced in one operation as a logging technique a resistivity log, a At log, a synthetic resistivity log and a differential resistivity log. A single bore hole exploring unit may be provided carrying the electrodes 27 and 29 along with acoustic transducers 10 and 12 simultaneously to probe the formations electrically and acoustically. Alternatively an acoustic logging tool alone may be utilized to produce a log of a velocity function and simultaneously to produce a synthetic resistivity function which itself may be a useful log and which may be compared with previously existing measured resistivity logs from the same bore hole. Further, resistivity functions and velocity functions previously measured by field techniques in the course of logging a bore hole may be utilized in connection with record playback techniques or other function generating devices to produce a synthetic log from already existing logs thereby more completely to describe the nature of the formations earlier logged.

Further it will be readily understood that all of the manipulative steps capable of being carried out by the apparatus as above described can be done by hand, utilizing as a basis of computations the Equations 1 or 2 in order to produce the synthetic functions and differential functions.

While in Fig. 1 a long normal electrode configuration has been illustrative, it will be understood that other configurations may be preferred in certain regions or areas where experience has proved them to yield resistivity measurements which more nearly conform to actual resistivity of the formations than obtainable through the use of long normal. Various multi-electrode systems are well known in the art. For example the seven-electrode system illustrated in Fig. 5 will be found preferable for use in logging bore holes wherein the drilling fluids are of low resistance, for example where cut by salt water and the like. While operation of the seven-electrode system, commonly referred to in the well logging art as the Laterolog, has been described in detail, Journal of Petroleum Technology" volume 192 (1951) at page 305, the features most pertinent to the present invention have been shown in Fig. 5. An A. C. current of constant intensity is fed from a source to a bore hole electrode 111. Electrodes 112, 113 and 114, 115 on the one hand and the monitoring electrodes 116, 117 and a surface electrode 118 are connected respectively to the input and output terminals of an automatic control apparatus 119. By this means a current is fed through electrodes 116 and 117 which continuously acts to maintain the difference of potential between electrodes 112, 113 and 114, 115 equal to zero. The common potential of electrodes 112, 113, 114, 115 is recorded by means of meter 121 or its equivalent with reference to an electrode. 122. By this means: the. sensed parameter is-dependent upon. current flowing, within a substantially horizontal sheet of space whose thickness is approximately equalto the spacing. 0.

In practice Laterologs are currently run with the spacing 0-0 of 32" with electrode 111 at the mid-point; When using such: a spacing in accordance with the present invention, it will be preferred that acoustic transducers trical function is illustrated and described in, detail. in

United States. Patent No. 2,535,666 to RobertA. Broding, a co-worker of applicant.

In accordance with the Broding system an elongated.

solenoid forms one arm of a bridge, network andis electromagnetically coupled to the adjacent formations. The

conductivity of theformations. is; one of. two factorsithat. is readily measured in the bridge network. For details, of operation of such system, reference should be had However in'accordance with the;

to the Broding patent. present invention, it should be noted that the length of the coil utilized for measuring conductivity controlling the effective penetration in the measurement of electrical resistivity bythe system shown in Fig 1 should be approximately equal to the separation between the acoustic.

transducers used, for example the separation between transducers 10 and 12 of Fig. 1. normal electrode configuration of Fig. l is to be utilized, the two bore hole. electrodes 27 and 29 should. be spaced approximately the. same distance apart as the acoustic transducers 10 and 12.

While a continuous acoustic well loggingsystcm would be. much preferred for use in obtaining a log; of a'velocity function,.other suitable methods may be utilized. For example incremental travel times may be obtained in the manner generically illustrated and described in Patent No. 2,503,904 to Dahrn, particularly to procedure outlined in; connection-with Fig. 6 wherein a plurality of detectors are positioned at spaced points; along the length of a bore hole and a single acoustic impulse: is produced by detonation of an explosive charge above or below the spaced. detectors. The arrival times of the.- acoustic energy' at the various detectors provide a ready indication of the incremental travel times along. the sec.- tion spanned by the array of detectors. generally is well understood by those skilled in the art and would be found entirely adequate for producing a velocity function suitable for utilization in the production of a synthetic log as above outlined.

While the: invention has been described and certain modifications. of apparatus suitable for carrying out the invention have been set forth in detail, it is to be. understood that further modifications may now suggest themselves to those skilled in the art and it is intended to. cover such modifications as fall within the scope. of the appended. claims.

What is claimed is:

l. The method of locating sections of earth formations having abnormal fluid content which comprises. generating. two electrical signals-which vary in relation to depth. below the earths surface in accordance. with twoearth parameters. one, of which is an electrical re.- sistivityfunction of the formations and the other an acoustic. velocity function-of said formations, generating.

Similarly if the long This procedure.

a. synthetic. signal in dependence. upon a mathematical power. function, an-assumed normal fiuidsaturation of the formations and one of said: electrical signals, andrecording as a function of depth of said formations said synthetic signal and the other of said electrical signals to indicate by departures therebetween the sections having said abnormal fluidsaturation.

2. The method oflocating sections of earth formations having abnormal fluid content which comprises generating two electrical signals which vary as a function of depth below the earths surface in accordance with two earth controlled parameters one of which is the. electrical resistivity. of the formations. and the other anacoustic. velocity function of said formations, simultaneously generating a synthetic signal in dependence upon, a mathematical-power function, an assumed normal. fluid saturation ofthe; formations, and one of "said electrical si'gnals, and. recording. as, functions of, depth saidv synthetic signal andthe other of said electrical sig;

" nalsto, indicate by departures. therebetween the sections,

having said. abnormal fluid saturation.

3.... The method of locating; sections of earth formations having. abnormal fluid content which comprises generating twoelectrical signals which vary as a function of depth below. the earths surface. in accordance with two earth parameters one of which is the electricalresisti'vity of the formationsandthc other an acoustic velocity function of said" formations, generating a synthetic signal in dependence upon a mathematical power function, an assumed" normal fluid" saturation of the formations and one of'said electrical signals, and, recording. the. difference between the other ofsaid electrical signals and said synthetic signal as a, function of depth.

4. The method of locating sections'of earth formations having abnormal fl'uidcontent which comprises generatingtwo electrical signals which vary as a function of depth below the earths surfacein accordance with two earth parameters one of which is the electrical resistivity of the formations and the'other an acoustic velocity functionof saidformations, simultaneously generating a" synthetic signal in dependence upon amathemati'cal powerfunc-tion, and assumed normal fluid saturation of the formations and one of said electrical signals, and recording the difference between the other of said electrical signals and said synthetic signal as a function of depth.

5. Themethod of producinga log of a-well bore in which variations in two physicalproperties, electrical re sistance and acoustic velocityof-theformations, are'encountered at various depths along the well bore which comprises generating a first electrical signalwhich varies along a scale proportional to depth below the earths surface: indirect relation to one of said two properties,

simultaneously generating a synthetic signal which nominal'ly corresponds with the other of'said two propertiesin dependence upon a mathematical power function, an assumed normal fluid saturation of the formations and said first signal, and recording said synthetic signal as a functionof depth whereby differences between said recorded signal-and a log of said second property directly indicate earth sections having abnormal fluid saturation:

6. The method-of producing a log of a well bore in which variations-in two physical: properties, electrical resistivity and. acoustic: velocity of "the formations are. encountered at.v-arious depths: along the well bore which comprises generating an electrical signal which varies. along a scale proportional'to depth belowthe earths- 9 second property indicate earth sections having abnormal fluid saturation.

7. The method of producing a log of a well bore in which variations in two physical properties, electrical resistivity and acoustic velocity of the formations, are encountered at various depths along the well bore which comprises generating an electrical signal which varies along scfle proportional to depth below the surface of the earth in dependence upon said acoustic velocity, simultaneously generating a synthetic signal which nominally corresponds with said resistivity in the relationship,

K E K i 8 a Z V Z V [where: K] where: K is a constant dependent upon an assumed normal fluid saturation of the formations, V is said first signal, Z is depth and a is a constant, and recording said synthetic resistivity signal as a function of depth whereby differences between said recorded signal and a log of said second property indicate earth sections having abnormal fluid saturation.

8. A system [fgor] for locating sections of earth formations having abnormal fluid content which comprises bore hole sensing means for generating two electrical signals which vary in relation to depth below the surface of the earth in accordance with two earth parameters one of which is an electrical resistivity function of the formation and the other an acoustic velocity function of said formation, means coupled to said bore hole sensing system including a mathematical power function generator for generating a synthetic signal in dependence upon said mathematical power function and one of said electrical signals, means for modifying said synthetic signal in dependence upon an assumed normal fluid saturation of the formations, and means for recording said modified synthetic signal and the other of said electrical signals as a function of depth to indicate by departures therebetween earth sections of said abnormal fluid saturation.

9. A system for locating sections of earth formations having abnormal fluid content which comprises bore hole sensing means for generating two electrical signals which vary in relation to depth below the surface of the earth in accordance with two earth parameters one of which is an electrical resistivity function of the formation and the other an acoustic velocity function of said formation, means coupled to said bore hole sensing system including a mathematical power function generator for generating a synthetic signal in dependence upon said mathematical power function and one of said electrical signals simultaneously with the generation of said two electrical signals, means for modifying said synthetic signal in dependence upon an assumed norrnal fluid saturation of the formations, and means for recording said modified synthetic signal and the other of said electrical signals as a function of depth to indicate by departures therebetween earth sections of said abnormal fluid saturation.

10. A system for locating sections of earth formations having abnormal fluid content which comprises bore hole sensing means for genera-ting two electrical signals which vary in relation to depth below the surface of the earth in accordance with two earth parameters one of which is an electrical resistivity function of the formation and the other an acoustic velocity function of said formation, means coupled to said bore hole sensing system including a mathematical power function generator for generating a synthetic signal in dependance upon said mathematical power function and one of said electrical signals, means for modifying said synthetic signal in dependence upon an assumed normal fluid saturation of the formations, and means coupled to said bore hole sensing system and to said modifying means for recording the difference between said modified synthetic signal and the other of said electrical signals as a function of bore hole depth to indicate by departures therebetween earth sections of said abnormal fluid saturation.

synthetic resistivity signal:

ll. A system for locating sections of earth formations having abnormal fluid content which comprises bore hole sensing means for generating two electrical signals which vary in relation to depth below the surface of the earth in accordance with two earth parameters one of which is an electrical resistivity function of the formation and the other an acoustic velocity function of said formation, means coupled to said bore hole sensing system including a mathematical power function generator for generating a synthetic signal in dependence upon said mathematical power function and one of said two electrical signals simultaneously with the generation of said two electrical signals, means for modifying said synthetic signal in dependence upon an assumed normal fluid saturation of the formation, and means coupled to said bore hole sensing system and to said modifying means for recording the difference between said modified synthetic signal and the other of said two electrical signals as a function of bore hole depth to indicate by departures therebetween earth sections of said abnormal fluid saturation.

12. A system for producing a log of a well bore in which variations in two physical properties, electrical resistance and acoustic velocity of the formations, are encountered which comprises bore hole sensing means for generating an electrical signal which varies in relation to depth below the surface of the earth in accordance with one of said two properties, means coupled to said bore hole sensing system including a mathematical power function generating means for generating a synthetic signal in dependence upon said mathematical power function and said signal, means for modifying said synthetic signal in dependence upon an assumed normal fluid saturation of the formations, and means for recording said modified. synthetic signal as a function of depth whereby diflerences between said recorded signal and a log of the other of said two physical properties directly indicate earth sections having abnormal fluid saturation.

13. A system for producing a log of a well bore related to the values of two physical properties, electrical resistance and acoustic velocity of the formations, which comprises sensing means for generating a first electrical signal which varies in relation to depth in said well bore in accordance with one of said two properties, means including a mathematical power function generating means for generating a synthetic signal in dependence upon said mathematical power function and said first signal, means for modifying said synthetic signal in dependence upon an assumed normal fluid saturation of said formations, and means for measuring differences between the values of the modified synthetic signal at points along said well bore and values of the other of said two properties at corresponding points for directly indicating earth sections having abnormal fluid saturation.

14. A system for producing a log of a well bore related to the values of two physical properties, electrical resistance and acoustic velocity of the formations, which comprises bore hole sensing means for generating a first electrical signal which varies in relation to bore hole depth in accordance with the one of said two properties, means coupled to said bore hole sensing means including a mathematical power function generating means for generating a synthetic signal in dependence upon said mathematical power function and said first signal, means for modifying said synthetic signal in dependence upon as assumed normal fluid saturation of said formations, and means coupled to said modifying means for measuring differences between the values of the modified synthetic signal at points related to different depths of said sensing means and values of the other of said two properties at corresponding points for directly indicating earth sections having abnormal fluid saturation.

No references cited. 

